Q: Compute d/dx∫₀ˣt²dt and ∫₁²(3x²)dx via FTC. FTC1: d/dx∫₀ˣt²dt = x² (differentiation undoes integration!). FTC2: antiderivative x³: 8-1 = 7. Check: ∫₁²3x²dx = [x³]₁² = 7 ✓! (FTC links the two calculus halves!)